I hope Freddie is doing ok. Have you contacted your vet? What did they say? Do you have an idea how long was the string? If it gets tangled up in his intestines you will probably need surgery to remove it. Keep a watchful eye on Freddie incase it becomes critical. I had a close call with my little one. I caught it in time. I was lucky. After that I removed everything in the house that was string like. Also, cats like dental floss. Make sure he can’t get that either.
You should call the Vet immediately, they can take an xray and see what's happening.
You can wait for it to pass...fingers crossed...but a visit and x-ray might give you peace of mind.
Years ago I gave my cat Gabe a chicken wing thinking he would just gnaw on it, he swallowed the entire thing and I called the Vet for advice. He gave me some things to look out for and Gabe passed it uneventfully but sure gave me a scare.